Disjunctive Total Domination Subdivision Number of Cycle and Wheel Related Graphs

A set $S \subseteq V(G)$ is a disjunctive total dominating set of $G$ if each vertex $u \in V(G)$ is either adjacent to a vertex in $S$ or is at distance two from at least two vertices in $S$. The minimum cardinality of a disjunctive total dominating set is the disjunctive total domination number. The disjunctive total domination subdivision number is the minimum number of edges that must be subdivided (each edge can be subdivided at most once) to increase the disjunctive total domination number of $G$. In this paper, we investigate the disjunctive total domination and its corresponding subdivision number for various cycle related graphs, including generalized fan, claw-free, and $k$-pyramid graphs. Furthermore, we extend our study to wheel related structures such as gear, helm, and web graphs.